Mechanical Engineering > GATE 2025 > Gears
A pair of spur gears is required to maintain a velocity ratio of 1:2. The module of the gears is 10 mm and the addendum is 10 mm. If the operating pressure angle is 15° the minimum number of teeth required on the pinion to ensure NO interference/undercutting is ______ (answer in integer).
Correct : 9
The minimum number of pinion teeth to avoid interference is given by:
Tmin = 2a / [m(√(1 + G(G+2)sin2φ) - 1)]
where a = addendum = 10 mm, m = module = 10 mm, G = gear ratio = 2, φ = 15°.
sin 15° = 0.2588, sin215° = 0.06699
√(1 + 2×4×0.06699) = √1.536 ≈ 1.239
Tmin = 2/(1.239 - 1) = 2/0.239 ≈ 9 teeth
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